Products of squares in finite simple groups

Martin W. Liebeck; E. A. O'brien; Aner Shalev; Pham Huu Tiep

doi:10.1090/S0002-9939-2011-10878-5

Products of squares in finite simple groups

Martin W. Liebeck, E. A. O'brien, Aner Shalev, Pham Huu Tiep

Einstein Institute of Mathematics

The Hebrew University of Jerusalem

Research output: Contribution to journal › Article › peer-review

Abstract

The Ore conjecture, proved by the authors, states that every element of every finite non-abelian simple group is a commutator. In this paper we use similar methods to prove that every element of every finite simple group is a product of two squares. This can be viewed as a non-commutative analogue of Lagrange's four squares theorem. Results for higher powers are also obtained.

Original language	English
Pages (from-to)	21-33
Number of pages	13
Journal	Proceedings of the American Mathematical Society
Volume	140
Issue number	1
DOIs	https://doi.org/10.1090/S0002-9939-2011-10878-5
State	Published - 2012

All Science Journal Classification (ASJC) codes

General Mathematics
Applied Mathematics

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10.1090/S0002-9939-2011-10878-5

Cite this

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title = "Products of squares in finite simple groups",

abstract = "The Ore conjecture, proved by the authors, states that every element of every finite non-abelian simple group is a commutator. In this paper we use similar methods to prove that every element of every finite simple group is a product of two squares. This can be viewed as a non-commutative analogue of Lagrange's four squares theorem. Results for higher powers are also obtained.",

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AU - Shalev, Aner

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AB - The Ore conjecture, proved by the authors, states that every element of every finite non-abelian simple group is a commutator. In this paper we use similar methods to prove that every element of every finite simple group is a product of two squares. This can be viewed as a non-commutative analogue of Lagrange's four squares theorem. Results for higher powers are also obtained.

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DO - 10.1090/S0002-9939-2011-10878-5

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SP - 21

EP - 33

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

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Products of squares in finite simple groups

Abstract

All Science Journal Classification (ASJC) codes

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